Limited Dependent Variable Models

Question 1

What are Limited Dependent Variable Models (LDV)?

Answer 1

LDV models are used when the dependent variable has a restricted range, such as binary outcomes (0 or 1), categorical choices or variables with many zero values but some positive outcomes.

Question 2

Give an example of a binary dependent variable.

Answer 2

Loan approval (1 = approved, 0 = rejected)

Question 3

What is the Linear Probability Model?

Answer 3

The LPM is an OLS regression model applied to a binary dependent variable, estimating the probability of an event happening based on explanatory variables.

Question 4

What is a major disadvantage of the Linear Probability Model?

Answer 4

The LPM can predict probabilities outside of the valid range (0-1), which is not realistic.

Question 5

Why are Logit and Probit models preferred over the Linear Probability Model?

Answer 5

Logit and Probit models ensure that predicted probabilities stay between 0 and 1, addressing the key issue with the LPM.

Question 6

What type of functional form do Logit and Probit models use?

Answer 6

Both Logit and Probit use a nono-linear functional form. Logit uses a logistic function and probit uses the cumulative normal distribution function.

Question 7

What estimation method is used for Logit and Probit models and why can’t we use OLS?

Answer 7

Maximum Likelihood Estimation (MLE) is used because these models are non-linear and therefore, OLS is not suitable.

Question 8

What is an Average Marginal Effect?

Answer 8

The AME is the average effect of a one-unit change in an explanatory variable on the probability of the dependent variable being 1.

Question 9

What is the Tobit model used for?

Answer 9

The Tobit model is used for censored dependent variables that have many zeros and some positive values, such as charity contributions.

Question 10

How does the Tobit model differ from OLS?

Answer 10

The Tobit model adjusts for the fact that the dependent variable is censored at zero, while OLS can predict negative values for variables that should be non-negative.

Question 11

What is latent variable in the context of LDV models?

Answer 11

A latent variable is an unobserved variable that influences the observed outcomes in models like Probit or Tobit.

Question 12

Why can’t we use OLS for binary or limited dependent variables?

Answer 12

OLS can predict invalid values for binary variables and does not handle censoring or non-linearity appropriately for limited dependent variables.

Question 13

In which case would you use the Tobit model instead of Logit or Probit?

Answer 13

the Tobit model is used when the dependent variable is continuous but censored at zero.

Question 14

How do Logit and Probit models handle predicted probabilities compared to LPM?

Answer 14

They use non-linear functions to ensure predicted probabilities are always between 0 and 1.

Question 15

What is the main disadvantage of Logit and Probit models compared to LPM?

Answer 15

Logit and Probit models are harder to interpet than LPM, especially for marginal effects and when there are many fixed effects or instrumental variables.

Question 17

What is the latent variable interpretation of the Probit model?

Answer 17

In the Probit model, we assume there is an underlying continuous latent variable and the observed binary outcome is a result of whether this latent variable crosses a threshold.

Question 18

What are the major advantages of Maximum Likelihood Estimation in LDV models?

Answer 18

MLE provides more accurate estimates for non-linear models like Logit and Probit, and it ensures that probabilities are properly restricted to the 0-1 range.

Question 19

How do you interpret coefficients in a Tobit model?

Answer 19

Tobit coefficients are similar to OLS, but are adjusted by the probability that the outcome variable is greater than zero, accounting for the censoring of the dependent variable.